Thursday, June 24, 2021

Portfolio Optimization Errors

A friend of mine likes to save money by ordering items in the U.S. and driving across the border to pick them up.  The trouble with his claim of having saved $50 on some order is that he ignores his car costs and the value of his time.  This mistake of leaving out important considerations because they are hard to value accurately creeps up in many decisions.

A group of my golfer friends like to figure out whether to buy a golf membership or not.  If the membership is $2400 and an average round costs $40, they reason that they need to play 60 rounds to break even on a membership.  However, getting a membership gives access to regular social functions.  This social consideration could easily be worth a lot to some people, and could even be a negative for others.  It’s also valuable to be able to start playing when the weather is iffy without worrying about losing money if the round has to be abandoned.  Some members even play more often than they really want to so they can justify the cost of a membership.  It’s better to come up with a roughly correct answer that takes into account all important factors than it is to come up with an exact answer that leaves out relevant considerations.

Whenever I see someone declare something like “I calculated that REITs should be 18.5% of my portfolio,” it’s obvious that relevant factors have been ignored.  We can’t know the exact future distribution of asset class returns.  Any attempt to use mean-variance optimization or some other optimization technique necessarily ignores the fact that the future may not look exactly like the past.

There’s nothing wrong with using past returns as a guide to the future, but we also need to think through other possibilities.  We could have higher (or lower) inflation in the future than the average over some period of the past.  The four decade bull run in bonds could transition into a multi-decade bear market in bonds.  Tax rates could change.  Stocks could tank in a way we’ve never seen before.  We can’t optimize for all these possibilities, but we can try to choose a plan where we’ll come out okay across all reasonably likely outcomes.  Thinking this way is very different from using guessed correlation figures to calculate perfect portfolio percentages.

Another mistake I see among those seeking the perfect portfolio is frequent tweaking to take into account new information.  These investors seem to think each portfolio change they make will be the last because their portfolio is finally perfect.  But then they learn something new that leads to more changes.  For some, all the adjustments become a form of buy high and sell low as they constantly shift toward whichever asset performed well recently and has a good story.

An area where I had to let go of trying to be perfect was in my asset location choices.  I have a set of rules for which types of accounts hold which asset classes.  For example, I try not to hold any fixed income in my RRSPs.  However, when it comes time to rebalance my portfolio, sometimes it’s just easier to buy some short-term bonds in my RRSP.  I still mostly stick to my asset location rules, but I’m not strict about it.  Any losses I suffer from not having a perfect portfolio are small compared to the peace of mind that comes from not worrying about small things.  This frees me to think about more important issues, like the possibility that the U.S. might change inheritance tax rules for Canadians who hold U.S. assets.

In summary, it’s much better to think about all the important factors in any choice, including those that are hard to quantify, than it is to calculate the easy-to-quantify factors to three or four decimal places.


  1. Hi Michael, when you say you try not to hold any fixed income in your RRSPs, are you referring to interest bearing investments? I would've thought that the RRSP is the ideal place for such holdings.

    It seems clear to me that a taxable account is the worst place for such investments due to high taxes paid on interest. Whether to hold them in TFSA or RRSP may be splitting hairs, and in the spirit of this post, perhaps not something worrying much about. But you consistently have good analytical insight, so I have to probe further!

    If I have to decide between two asset classes that could be held in either TFSA or RRSP, my inclination is to place the asset class with a lower expected return in the RRSP. If the actual return is in fact lower, it means that I have less to withdraw from my RRSP in retirement and I will pay less taxes. If the actual returns invert relatively speaking to their expected returns, then I lose, but I played the odds. Do you see a flaw with this line of reasoning? Maybe the wording I used sounds like gambling, but I don't think it is, it's just improving my overall expected return.

    On the other hand, a problem with the TFSA is that there aren't many options for what can be held in it without running into withholding tax penalties that can be avoided in an RRSP account. I have a broad market Canadian ETF and a broad market international ETF (a Canadian ETF which holds individual securities, not a wrapper of other ETFs) in my TFSA. Those are the only two components of my portfolio I hold in my ETF. The rest are better off in my RRSP because of withholding tax penalties.

    I don't actually have any fixed income in my portfolio yet, but I may at some point.

    1. This is exactly the sort of thing, where you have part of the story and optimize sub-optimally!

      The RRSP is a tax shelter, so why would you try to put your lowest-returning assets inside it? Well, if you forget to adjust for the fact that it's pre-tax money that's in there, running a scenario to try to optimize asset location will tell you to do just that -- and there are many, many articles out there that get this wrong.

      Similarly, focusing on tax efficiency in isolation says that bond returns are taxed at the highest rate, so you might conclude that you want to prioritize sheltering those. But bond returns are also super-low right now, so the tax savings in dollars one way or the other is also low -- you're better off sheltering your higher-expected-return equities.

      Michael's written about this a few times, here's one example to look at:

    2. @Potato, I think I agree with you, but for the most part, I still have the same question I originally had.

      After reading the post you linked, I relized I'd read it before. I'm a firm believer in ATAA. I think it's a mistake to ignore the taxes you'll pay when drawing from your RRSP in retirement. Any guess will be wrong, but assuming 0% is worse than almost any other reasonable number. I assume my TFSA dollars are worth 50% more than my RRSP dollars, which is another way of assuming a 33% tax on my RRSP dollars. Maybe that's high. But I don't see taxes going down any time soon, and I'm still ~20 years from retirement.

      The part of my original post I need to think about more is "It seems clear to me that a taxable account is the worst place for [interest bearing] investments due to high taxes paid on interest". This is far from clear to me now, and I'll give it more thougt. It's true that you lose a larger percentage of interest gains in taxable accounts, but the closer those gains are to zero, the less you care about what fraction of those gains are lost.

      If we ignore taxable accounts for the timebeing (I don't hold any investments in taxable accounts), I was primarily focused on the decision of bonds in TFSA vs. RRSP. The ATAA post you linked to doesn't really cover this as it focuses on bonds in RRSP vs. taxable accounts. I'm wondering if my original logic still holds on putting bonds in TFSA vs. RRSP. Both are tax sheltered investments. If we ignore withholding taxes (which can't be ignored entirely), my total tax shelter available is my RRSP + TFSA. Wouldn't I still want my bonds to be located in my RRSP rather than my TFSA?

      Let's consider an example where:
      * My portfolio is 50% bonds and 50% stocks
      * Bonds return 2%, stocks return 6%.
      * My marginal tax rate while working is 50% (so I can choose to put $2 in an RRSP or $1 in a TFSA).
      * My marginal tax rate in retirement is 33%.

      Let's suppose in my first I have $4,200 to invest. To put "half into bonds and half into stocks", I put $3,600 into bonds in the RRSP and $2,400 into stocks in the TFSA. Now I'm $1,800 short(!) but thankfully by tax refund on the $3,600 RRSP constribution covers that. Based on my assumption of 33% tax in retirement, I am equally weighted in after tax dollars in stocks and bonds.

      This is my first year investing, but let's just assume I do nothing else and let it grow. I recognize this is a gross assumption since I would need to rebalance as my asset balance changes, I will continue to contribute over the years, etc. But I *think* this is a reasonable assumption to illustrate the RRSP vs. TFSA decision for bonds. Another assumption I'm making is that it is my marginal tax rate in retirement that matters. Again, I think this is the right call as subtle shifts are likely to keep you close to the same bracket, and differential dollars to be taxed would be taxed at the marginal rate. Effective tax rates (factoring various clawbacks) in retirement are a tricky thing and require some careful consideration of their own, but I don't think they need to be considered here.

      After 30 years:
      * The $3,600 in bonds grows to $6521. Assuming the marginal rate on withdrawl (since this is now part of a bigger portfolio and is drawn out over many years, let's just use the marginal rate), this is worth $2913 in after tax dollars.
      * The $2,400 in stocks grows to $13,784 and has no tax payable.
      * Overall, I have $20,305 in after tax dollars.

      What if I did it the other way?
      * The $2,400 in bonds grows to $4347 in the TFSA.
      * The $3,600 in sotcks grows to $20,676 in the RRSP. After paying 33% tax, this is $13,853.
      * Overall, I have $18,201.

      This seems to show it is best to put the bonds into the RRSP's.

      Having said all of this, if you have room to put *both* into your RRSP, I think you're better off doing that. I'm close to the limit on both types of accounts; maybe this isn't very typical.

    3. Hi Returns Reaper,

      In your example, you didn't discount the RRSP bonds by 1/3. The after tax value if the bonds works out to $4347, the same as the bonds-in-TFSA case. The after-tax value of the stocks is also the same in both cases ($13,784) if we ignore the rounding difference between 1/3 and 33%. So, in this example, we have no preference between RRSP and TFSA for stocks and bonds. In reality of course, the difference in U.S. dividend withholding taxes matters.

      Comparing either RRSPs or TFSAs to taxable accounts gives different results. In this case, it's preferable to hold bonds in the taxable account and stocks in the RRSP or TFSA.

      In your first comment, I think where you went astray was to focus on the amount of tax you pay. You do indeed expect to pay more tax by holding stocks in an RRSP and bonds in a taxable account compared to the reverse. But you also end up with more for yourself.

      The resolution of this seeming paradox comes from the fact the the final portfolio size is different for the two scenarios when viewed in before tax terms. By owning more stocks (before tax) in the stocks-in-RRSP scenario, you end up with a larger portfolio after 30 years. This excess gets split between you and CRA.

    4. Another thing to consider in your analysis is how the taxable income from an RRSP could impact income from GIS on one end of the scale, and OAS on the other. With years to go, it’s unlikely that GIS will be a concern for you, but OAS clawback might be.

    5. Hi Bob,

      Good points. I think of the effects on GIS and OAS as part of the tax rate (even though CRA doesn't call them taxes). So, when I calculate expected taxes during retirement, I factor in GIS and OAS.

  2. Hi Michael, you're absolutely right that my math is messed up with bonds when they were in the RRSP. So, as you pointed out, with the assumptions I made in my scenario it makes no difference whether bonds are in the TFSA or RRSP. Thanks for catching my error!

    This means it is largely down to a coin toss. To Bob's point, it seems like you might as well put them in the RRSP, unless there is a taxable account involved.

  3. Returns Reaper, Until recently, I too only had tax sheltered accounts. When I read your post, I was impressed with the fact that you are aware that TFSAs are treated differently than RRSPs when it comes to US dividends. I thought you made some good points and since I am now drawing my income from my RRSPs (now RRIFs), my strategy is to deplete them as quickly as possible while trying to keep my taxable income at the same level that it was when the investments were made. You seem to have grasped this idea early enough to not make some of the mistakes I did.